Typical distances in ultrasmall random networks

Details Typical distances in ultrasmall random networks Typical distances in ultrasmall random networks

2011-02-28

arxiv.org/abs/1102.5680v1

Mathematics

Probability

16 pages

Scientific paper

We show that in preferential attachment models with power-law exponent $\tau\in(2,3)$ the distance between randomly chosen vertices in the giant component is asymptotically equal to $(4+o(1))\, \frac{\log\log N}{-\log (\tau-2)}$, where $N$ denotes the number of nodes. This is twice the value obtained for several types of configuration models with the same power-law exponent. The extra factor reveals the different structure of typical shortest paths in preferential attachment graphs.

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